Magnetic and electric fields of direct currents in a layered earth (short note)

Abstract

We derive a numerical solution of the steady-state magnetic field due to a DC current source in a layered earth model. Such a solution is critical for interpretation of magnetometric resistivity (MMR) data. Our solution is achieved by solving a boundary value problem in the spatial wavenumber domain and then transforming back to the polar spatial domain. The propagator matrix technique is used to interrelate solutions between layers. Two simplified cases are examined to promote understanding of the magnetic fields. In particular, the derived formula illustrates why surface MMR data are insensitive to 1D conductivity variations and why borehole measurements are effective in finding conductivity contrasts.